The detection of GW signals is performed by monitoring the change in the relative distance between the mirrors, measured as a change in the phase of the laser beams [1]}. Therefore, any fluctuation in the thickness or in the optical properties of the coating materials acts like a spurious displacement noise. Thermo-refractive and thermo-elastic fluctuations are not relevant [2]}, and the dominant source of phase noise is due to the Brownian motion of all the layers. The fluctuation dissipation theorem [3]} links Brownian noise to the rate of energy dissipation in the coating material due to internal friction. The amount of friction is measured by the material loss angle \(\varphi \) , that is the fraction of energy lost per cycle when the material is driven by a sinusoidal external force. In the coating materials used so far, the worst offender is tantala-titania, with measured values \((2.3-3.4) \times 10^{-4}\)  [4]}, [5]}. The silica layers have one order of magnitude lower loss angle, \((2.3-4.0) \times 10^{-5}\)  [6]}, [5]}.
